Measuring Capital Stocks and Capital Services in Switzerland

Rudolf, Barbara; Zurlinden, Mathias Article Measuring Capital Stocks and Capital Services in Switzerland Swiss Journal of Economics and Statistics Provided in Cooperation with: Swiss Society of Economics and Statistics, Zurich Suggested Citation: Rudolf, Barbara; Zurlinden, Mathias (2009) : Measuring Capital Stocks and Capital Services in Switzerland, Swiss Journal of Economics and Statistics, ISSN 2235-6282, Springer, Heidelberg, Vol. 145, Iss. 1, pp. 61-105, https://doi.org/10.1007/BF03399275 This Version is available at: https://hdl.handle.net/10419/185909 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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We thank the Editor (Klaus Neusser) and two anonymous referees for this Journal and the SNB Working Paper Series for helpful comments and suggestions. We also thank Gregory Rais, Eveline Ruoss and Elizabeth Steiner for comments on an earlier version and Yves Blattmann for providing valuable research assistance. The views expressed in this paper are our own and do not necessarily reflect the position of the Swiss National Bank. Measuring Capital Stocks and Capital Services in Switzerland Barbara Rudolf and Mathias Zurlinden* JEL-Classification: C43, D24, D92, E22 Keywords: capital stock, capital services, ICT goods 1. Introduction Measures of capital are used for many different purposes and the appropriate definition may differ, depending on the issue in question. In a wealth context, the capital stock is the stock of physical assets existing at a point of time. From a production perspective, however, capital services is the flow of services generated by these assets during a given period. Capital stocks and capital services denote two different but interrelated concepts of capital. On the one hand, capital services are derived from the stock of capital installed. On the other hand, the value of the capital stock reflects the discounted flow of future capital services. The theory underlying the measurement of capital services was developed by Dale Jorgenson and co-authors in the 1960s. Jorgenson (1963) and Hall and Jorgenson (1967) showed how service prices, also called the user cost of capital, can be derived, even though they can not be observed directly. Jorgenson and Griliches (1967) and Jorgenson and Christensen (1969) developed the application of user cost of capital to the calculation of measures of capital input. Since then, the literature has grown rapidly. Jorgenson (1989), Hulten (1990), and Diewert and Schreyer (2006) provide excellent introductions. Practical guidelines for estimation can be found in two manuals published by the Organization for Economic Co-operation and Development (2001a, 2001b), and in Schreyer, Diewert and Harrison (2005). 62 Rudolf / Zurlinden So long as the aggregate capital stock consists of a single type of capital goods, the capital stock and the flow of capital services will grow at the same rate over time. This follows from the conventional assumption that the capital services provided during a given period are proportional to the stock at the end of the previous period. Differences between the two measures of capital become more interesting when capital goods are heterogenous (as in reality they are). Information and communication technology (ICT) goods, for example, have shorter asset lives than buildings, and the relative price of ICT goods has fallen substantially over time. Under these circumstances, growth rates of the aggregate capital stock will differ from those of the flow of aggregate capital services. The differences can be traced back to the asset price to service price ratios associated with the various types of capital goods. To make full use of these possibilities, we need investment data that do justice to the heterogeneity of capital goods. For many years, the National Accounts for Switzerland offered little detail, as gross fixed investment was broken down into not more than two categories – equipment and structures. The situation has improved with the publication of the National Accounts according to the international standard SNA93 in December 2003 (ESVG95). For investment, the move from ESVG78 to ESVG95 brought the widening of the definition of gross equipment investment (inclusion of computer software, in particular) and the breakdown of the data into nine categories for equipment and three categories for structures. The annual series for these twelve categories are available for the period from 1990 onwards. In this paper, we present a set of measures of capital services and the net (wealth) capital stock for the aggregate Swiss economy. The net capital stock represents accumulated gross investment less accumulated depreciation. To simplify terminology, capital stocks henceforth are always net capital stocks. The range of assets considered is restricted to fixed produced assets. That is, we do not consider inventories, land, and intangible assets such as patents and trade marks. For both capital services and the capital stock, results are provided based on two different breakdowns of investment data: the 2-asset case drawing upon data for structures and equipment, and the 12-asset case drawing upon data for three categories of structures and nine categories of equipment. Reflecting data availability, the results cover the periods 1970–2005 (2-asset case) and 1990–2005 (12-asset case). The decision to calculate capital services for the 2-asset case results from the need to have access to time series reaching back beyond 1990. Moreover, it allows us to assess the effect of the heterogeneity of capital goods, as captured by the more detailed data available for 1990–2005. Measuring Capital Stocks and Capital Services in Switzerland 63 To explore the robustness of our measures of capital, we recalculate our results based on several sets of alternative assumptions. These assumptions concern the life span of the various types of assets, the starting values of the asset stocks, the method for calculating the user costs of capital, and the choice of price indices used to compute ICT investment volumes. In addition, quarterly measures of capital and estimates of capital services based on mid-year asset stocks are considered. The assessment of price indices focuses on ICT goods because of the rapid technological progress in this field, which makes the measurement of constantquality prices a difficult issue. Hedonic price indices are often recommended as an alternative to the conventional matched-model methods of quality adjustment. However, no such indices are compiled by statistical offices in Switzerland. We therefore make use of the hedonic price indices for ICT goods developed by the Bureau of Economic Analysis of the US Department of Commerce to examine the sensitivity of the results. In 2006, the Swiss Federal Statistical Office (SFSO) published estimates of growth in multi-factor productivity over the period 1991–2004 for Switzerland (see Swiss Federal Statistical Office, 2006a). These results are interesting for our purpose because they are based on estimates of growth in capital services. In preparing this paper, we have reviewed our earlier estimates of capital stocks and capital services in light of the SFSO publication. In consequence, we have adopted the SFSO assumptions on asset lives but continue to differ in other respects. Appendix C summarises the differences in method and data and compares the results. The paper is organised as follows. Section 2 provides a brief outline of the theory underlying the measurement of capital stocks and capital services. This is followed in Section 3 by the description of the data used to construct the annual series. Section 4 presents the results for the 2-asset case in the period 1970–2005. Section 5 presents the results for the 12-asset case in the period 1990–2005. Section 6 examines the sensitivity of the results to alternative sets of assumptions. Section 7 contains concluding remarks. Three appendices provide information on selected issues. Appendix A gives further detail on definitions and sources of the data used in the calculations. Appendix B provides the growth rates and the shares in profits and in wealth of the twelve types of assets considered in the period 1990–2005. Appendix C describes the differences between our calculations and those by the SFSO. 64 Rudolf / Zurlinden 2. The Measurement of Capital This section outlines the methodology of capital measurement. First, the perpetual inventory method is introduced (2.1). Then, aggregate capital services (2.2) and the aggregate capital stock (2.3) are derived. A brief review of aggregate rates of depreciation concludes the section (2.4). For a more detailed derivation of the results, see Jorgenson (1989) and Oulton and Srinivasan (2003). 2.1 The Perpetual Inventory Method The perpetual inventory method provides an approach for deriving estimates of the capital stock from the flow of investments for a given type of asset. The method starts off from a time series of investment volumes, which is obtained by deflating current-price investments with the appropriate price deflator. The price deflator should be a constant-quality price index so that all investment volumes are expressed in efficiency units of the year to which the price index is referenced (see Schreyer, Diewert and Harrison (2005, p. 25). Next, weights reflecting the age-efficiency profile are attached to each vintage. The age-efficiency profile describes how the efficiency of an otherwise homogenous asset changes with age. Finally, the weighted investment vintages are added together to give the capital stock. The stock of capital thus is a weighted sum of past investments, with weights corresponding to the efficiency of each vintage relative to that of the latest vintage. Several profiles of relative efficiencies have been discussed in the literature: geometric, straight-line, “one-hoss shay”, etc. With the “one-hoss shay” efficiency pattern, no loss in efficiency occurs during the lifetime of the capital good; a typical example is the light bulb. With the geometric and straight-line efficiency patterns, the efficiency of the capital good declines continuously. The geometric profile assumes that the efficiency declines at a constant rate, whereas the straight-line profile assumes that the efficiency declines by equal amounts in each period. Age-efficiency profiles may not be confused with age-price profiles, which describe how the price of a given type of asset declines with age (depreciation). Under general conditions, the two profiles are not identical. But they are related to one another because the price of an asset is the present value of the service flow generated by the asset over its lifetime. It can be shown that there is an age-price profile for each age-efficiency profile, and vice versa. In this paper, we assume the geometric model, which implies that the efficiency declines at a constant rate. The geometric model has the very useful feature that the age-efficiency profile coincides with the age-price profile. This simplifies the Measuring Capital Stocks and Capital Services in Switzerland 65 analysis and is a key reason for the widespread use of the model. Moreover, there is empirical evidence supporting the assumption of a geometric age-efficiency profile (see Hulten and Wykoff, 1996). The capital stock of asset type i at the end of period t, Ai,t, can now be written as 1 (1 ) , it it i it AI A , , ,− = + −δ (1) or 0 (1 ) , it i it AI ∞ β , , −β β= = −δ ∑ (2) where Ii,t denotes gross investment and δi is the rate of depreciation which equals the rate of decay when the geometric model is assumed. In practice, we often work with a starting value for the capital stock, Ai,0, yielding 1 0 0 (1 ) (1 ) . t t it i i it AA I − β , , , −β β= = −δ + −δ ∑ (3) 2.2 Shares in Profits and Aggregate Capital Services Moving from stocks to services, we assume that, for a given type of capital, capital services during period t are proportional to the underlying capital stock at the end of the previous period. Setting the proportionality factor equal to 1, this gives: 1 . it it KA , ,− = (4) Section 2.1 has focused on the aggregation across vintages of a given type of asset. If all assets were of the same type, we could leave it at that. However, capital assets are heterogenous and, consequently, there is the problem of aggregation of capital services across asset types. To aggregate capital services across types of assets, one needs information on the price of capital services, also called the user cost of capital. This is the rental price that has to be paid for the use of the capital goods during a given period. Generally, user costs of capital cannot be observed because most capital goods are utilised by the owner. However, in a competitive equilibrium, user costs of capital are linked to asset prices and therefore can be derived indirectly. The basic idea is that the equilibrium value of the implicit user cost must cover the opportunity 66 Rudolf / Zurlinden 1 See Diewert (2003) for various forms of the user cost of capital and for references to early contributions from Eugen Böhm-Bawerk, Léon Walras and others. cost of an investment plus the loss in the asset value. Ignoring adjustment costs and uncertainty, the arbitrage condition can be written as 10 0 1 10 , t it it it it rP U P P ,−, ,, ,, ,−, = +− (5) where Ui,t,0 is the user cost of a new (i.e. age 0) asset of type i payable at the end of the current period, rt is the nominal interest rate, Pi,t−1,0 is the price of a new i-type asset at the end of the previous period, and Pi,t,1 is the price of an i-type asset of age 1 at the end of the current period. From Equation (5), a convenient form of the user cost of capital can be derived by introducing depreciation and asset inflation. Depreciation is the reduction in the market price due to ageing. Assuming that the depreciation rate on a new asset, δi, does not vary over time, we have 10 (1 ) . it i it PP ,, ,, = −δ (6) Asset inflation, in turn, is the change in market prices for new assets between the end of period t − 1and t: 0 10 (1 ) , it it it P qP ,, , ,−, =+ (7) where qi,t is the rate of inflation for asset type i. Substituting Equations (6) and (7) into Equation (5), solving for the user cost of capital, and dropping the age subscripts gives 1 [ ], it t i it i it it U r q qP , , , ,− = +δ − +δ (8) where Pi,t−1 = Pi,t−1,0 and Ui,t = Ui,t,0. This is the user cost of capital formula of which several variants exist in the literature.1 Calculation of Ui,t requires information on the level and rate of change of prices for new assets, the depreciation rate and the rate of return. The prices for new assets are the investment price deflators. The depreciation rates correspond to the geometric rates that describe the age-efficiency patterns in Equation (1). And the rate of return, rt, can be derived from the equilibrium condition equating the total value of capital services to total profits, Πt. That is: Measuring Capital Stocks and Capital Services in Switzerland 67 1 11 [ ], mm t it it t i it i it it it ii UK r q q P K , , , , ,− , == Π = = +δ − +δ ∑∑ (9) where Πt is measured by data on property compensation. With the information on the capital services and the user cost of capital for each type of capital asset, we can aggregate capital services across asset types. The aggregation is done by the well-known Törnqvist-translog index. This implies that the growth rate of the volume of capital services is a weighted average of the growth rates of the services yielded by each asset, where the weights are the shares in the total value of capital services (i.e. in total profits): 11 1 ln( ) ln( ), m it t t it it i KK K K w − , ,− = /= / ∑ (10) where 1 1 , . 2 it it it it it m it it it i w w UK w wUK , ,− , , ,, ,, = + == ∑ (11) This completes our discussion of the theory underlying the measurement of capital services. The growth rates of the volume of capital services can be calculated based on Equations (1), (4), (8) and (10). Given total profits in a specific year, 1 , m t i it it UK =, , Π =Σ a series for capital services at chained prices of that year can be calculated. 2.3 Shares in Wealth and the Aggregate Capital Stock The aggregate capital stock is based on the market value of capital assets and corresponds to the wealth concept of capital. Because the stock of each type of asset is defined in units of new assets (see Equation (2)), the appropriate price indices are the deflators for investment. In the presence of quality changes, these should be constant-quality price indices. The procedure up to the aggregation over vintages for each type of asset is the same for the aggregate capital stock and for aggregate capital services. However, the aggregation differs in that the stocks are weighted by relative market prices to obtain the aggregate capital stock, whereas the services derived from the stocks are weighted by relative rental prices. 68 Rudolf / Zurlinden The growth rate of the aggregate capital stock can thus be written as a weighted average of the growth rates of the stocks of each asset, with weights corresponding to the shares in the value of total assets (i.e. in total wealth): 11 1 ln( ) ln( ), m it t t it it i AA A A v − , ,− = /= / ∑ (12) where 1 1 , . 2 it it it it it m it it it i v v PA v vPA , ,− , , ,, ,, = + == ∑ (13) Based on Equation (12) and the total value of the assets in a given year, 1 m i it it PA =, , Σ , a series for the capital stock at chained prices of that year can be calculated. 2.4 Aggregate Depreciation For many purposes, it is interesting to look at the aggregate rate of depreciation. With depreciation rates differing from one class of assets to another and the composition of the capital stock changing over time, the aggregate depreciation rate will change as well. The aggregate real rate of depreciation can be calculated based on the aggregate capital accumulation equation 1 (1 ) , R t t tt AI A − = + −δ (14) where It is aggregate real investment. Solving Equation (14) for R t δ gives 1 1 () . Rt tt t t I AA A − − −− δ= (15) As Oulton and Srinivasan (2003) pointed out, R t δ may be unbounded and therefore must be interpreted with care. To avoid this problem, we can calculate 1 1 1 1 , m i it it Ni m t it it i PA PA , ,− = , ,− = δ δ= ∑ ∑ (16) where N t δ is the aggregate nominal rate of depreciation. Measuring Capital Stocks and Capital Services in Switzerland 75 8 Strictly speaking, the data underlying the 12-asset case allows us to calculate aggregate capital stocks starting in 1990 and capital services starting in 1991. To facilitate comparison with other results presented in this paper, we have estimated capital services in 1990. According to Equations (8), (10) and (11), this requires estimates of the 12 investment price deflators in 1989. We have calculated these 12 values by approximating the 1990 rate of change of investment prices of the three components of structures and the nine components of equipment by the corresponding rate of change of total structures and total equipment, respectively. shown some tendency to rise, reflecting the fact that the stock of assets with short lives (equipment) has increased more rapidly than the stock of assets with long lives (structures). Table 2 shows that growth in the stock of structures exceeded growth in the equipment stock in the period 1970–1990 (3.30% and 2.50%). In the period 1990–2005, it is the other way round, with the equipment stock (2.50%) growing more rapidly than the stock of structures (1.67%). 5. The 12-Asset Case: 1990–2005 This section presents the benchmark results of aggregate capital services and the aggregate capital stock for the 12-asset case. The 12-asset case differs from the 2-asset case in that structures are broken down in three, equipment in nine categories. In addition, the detailed data underlying the 12-asset case are available from 1990 onwards only. Consequently, the results (and the comparison with the 2-asset case) refer to the period 1990–2005.8 In the 12-asset case, aggregate capital services have increased by 2.34% per year on average between 1990 and 2005. Capital services from structures have increased by 1.79%, capital services from equipment by 2.88%. The corresponding average growth rates of the aggregate capital stock are 1.78% for the total, 1.67 for structures, and 2.07% for equipment. Comparison with the results from the 2-asset case shows higher growth in aggregate capital services and lower growth in the aggregate capital stock (see Figure 3). Yet the pattern of growth rates does not differ greatly between the 2-asset and the 12-asset case. Overall, differences in the dynamics are more marked between capital services and the capital stock than between the 2-asset and the 12-asset case. Finally, we note again that aggregate capital services are more volatile than the capital stock. Because the asset stocks of structures and equipment are heterogenous in the 12-asset case, Figure 3 also exhibits the results for structures and equipment. The differences between the 12-asset case and the 2-asset case are negligible for 76 Rudolf / Zurlinden Figure 3: Capital Services and Capital Stock, Growth Rates, 12-Asset Case vs. 2-Asset Case all assets 0 1 2 3 4 5 6 7 Capital services, 12-asset case Capital services, 2-asset case Capital services, 12-asset case Capital services, 2-asset case Capital services, 12-asset case Capital services, 2-asset case 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 equipment –1 0 1 2 3 4 5 6 7 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 structures 0 1 2 3 4 5 6 7 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 Measuring Capital Stocks and Capital Services in Switzerland 77 Figure 3 (continued) all assets 0 1 2 3 4 5 6 7 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 equipment –1 0 1 2 3 4 5 6 7 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 Capital stock, 12-asset case Capital stock, 2-asset case Capital stock, 12-asset case Capital stock, 2-asset case Capital stock, 12-asset case Capital stock, 2-asset case structures 0 1 2 3 4 5 6 7 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 78 Rudolf / Zurlinden structures where we have assumed that asset lives are the same for all three categories. For equipment, on the other hand, the differences in results are notable suggesting that the composition of the equipment stock have significant effects on the aggregate measures of capital. To analyse the results in greater detail, it is interesting to look at the growth rates and at the shares in profits and in wealth of the various asset stocks (see Table 3 in the Appendix). The assets with the highest growth rates are software and computers. At the same time, software and computers are the assets with the highest rental price to asset price ratios, reflecting relatively short asset lives and a steep fall of their relative prices. This implies that the discrepancy between growth in aggregate capital services and growth in the aggregate capital stock is driven by these two types of assets. Nevertheless, the weights of computers and software in the aggregation of capital services and the capital stock are modest, despite some substantial gains during the period 1990–2005 in the case of software. The share in profits, wi,t, increased from 3.3% in 1990 to 6.1% in 2005 for software, whereas it declined from 3.5% to 3.2% for computers. For the share in wealth, vi,t, the changes are from 0.6% to 1.2% and from 1.0% to 0.8%, respectively. Figure 4: Aggregate Depreciation Rate, 12-Asset Case, Nominal and Real 0.080 0.075 0.070 0.065 nominal real 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 The nominal and the real aggregate depreciation rate are shown in Figure 4. Both rates have increased since the mid-1990s which implies that the stock of assets with short service lives has grown more rapidly than the stock of the assets with longer asset lives. The size of the increase is larger for the real rate than for the nominal rate, and larger in the 12-asset case than in the 2-asset case. Measuring Capital Stocks and Capital Services in Switzerland 79 6. The Effect of Alternative Assumptions The results presented in Section 4 and Section 5 are based on a number of assumptions which may or may not be accurate. In this section, we examine the robustness of the results by presenting measures of aggregate capital services and the aggregate capital stock which are based on alternative sets of assumptions. The first two sets of alternative assumptions concern the starting values of asset stocks (Section 6.1) and the service lives of assets (6.2). Then the method for calculating the user cost of capital (6.3) and the role of ICT prices (6.4) are considered. The former is examined by introducing exogenous (instead of endogenous) rates of return and real (instead of nominal) user cost of capital. The latter is explored by recalculating volumes and weights of ICT assets based on hedonic US price indices. Finally, we look at capital services based on mid-year asset stocks assuming that investment is spread evenly over the year (6.5) and based on quarterly estimates of capital stocks and capital services (6.6), two variants that are particularly useful in applied empirical work. It can be shown that when the economy moves along the steady-state path, with constant relative prices and all classes of investment growing at the same constant rate, growth in capital services and growth in the capital stock correspond to growth in investment, and factors like starting values, service lives or methods for calculating the user cost of capital do not affect the results. It is unrealistic, however, to assume that the economy moved along the steady state in the period under review, and therefore it is reasonable and necessary to examine the robustness of the results. 6.1 Starting Value As described in Section 3, the starting values of all asset stocks, Ai,0, are calculated based on artificial data. To examine the effect of these starting values, we now raise the 1947 values of total equipment and total structures by 100%. Figure 5 shows the results for aggregate capital services and the aggregate capital stock in levels and growth rates over the period 1970–2005. The benchmark results from Section 4 are given for comparison. The results in levels show that raising the starting values of the asset stocks results in higher levels of the aggregate capital stock in subsequent years. However, the gap between the alternative series and the benchmark series is narrowing over time. For aggregate capital services, in contrast, the alternative series intersects with the benchmark series in 1990. This reflects the construction of the series, with total capital services set equal to total profits in 1990. 80 Rudolf / Zurlinden The dynamics of our two measures of capital are little affected by the doubling of the starting values. This reflects the substantial net investment that took place from 1948 to 1970. In 1970, only 1% of the equipment capital stock and 13% of the structures capital stock consisted of investment vintages 1947 or older. Overall, the effect of the change in starting values on growth rates appears to diminish rapidly over time. As an alternative to linear changes in starting values, we can examine the effect of starting values calculated with different methods. Two additional sets of starting values are considered. First, the estimates by Goldsmith (1980) for stocks of equipment and structures in 1948, recalculated at 1990 prices, are used as starting values for 1948. Second, estimates based on the steady-state approach are used as starting values for the stocks in 1947. The steady-state approach can be derived from the perpetual inventory equation. Rewriting Equation (1) as 1 11 it it it it i it it AA I gAA , ,− , , ,− ,− − = =−δ + (17) and solving for the capital stock Ai,t−1 gives 1 it it i it I Ag , ,− , =. δ+ (18) Along the steady-state growth path, the growth rate of the capital stock, gi,t, equals the growth rate of type-i investment. But the economy was hardly in the steady state in 1948. Therefore, following Kamps (2006), we set gi,1948 to the average annual growth rate of type-i investment over the period 1948–2000, and Ii,1948 to its Hodrick-Prescott filtered (λ = 100) own value. It turns out that the resulting starting values deviate moderately from the values used in the calculations reported in Section 4. Goldsmith’s (1980) estimates are 33% lower for structures and 27% lower for equipment than our 1948 values. The starting values obtained from the steady-state approach, in turn, are 15% lower for structures and 13% lower for equipment than our 1947 values. Thus, the results for the aggregate capital services and the aggregate capital stock based on these two alternative sets of assumptions are closer to the benchmark series reported in Section 4 than what is shown in Section 5 for the case with starting values raised by 100%. Measuring Capital Stocks and Capital Services in Switzerland 81 Figure 5: Effect of 100% Increase in 1947 Asset Stocks on Capital Services and Capital Stock, 2-Asset Case 40 60 80 100 120 140 160 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02 04 × 1,000 40 60 80 100 120 140 160 707274767880828486889092949698000204 × 10,000 0 1 2 3 4 5 6 7 Capital services, growth Capital services, growth (benchmark) 707274767880828486889092949698000204 0 1 2 3 4 5 6 7 707274767880828486889092949698000204 Capital services Capital services ( benchmark) Capital stock Capital stock (benchmark) Capital stock, growth Capital stock, growth (benchmark) 82 Rudolf / Zurlinden 9 The results reported in this section are based on the 1947 starting values used in Section 4. The results do not change significantly when these starting values are re-calculated based on the depreciation rates resulting from the longer asset lives assumed here. 6.2 Service Lives and Depreciation Rates Assumptions concerning the lives of assets vary a great deal from one country to another. As Oulton and Srinivasan (2003) pointed out, these variations probably reflect differences in methodology rather than real economic differences. In this paper, we have opted for the asset lives used by the Swiss Federal Statistical Office (2006b) which in turn are based on an assessment of what is used by other countries. In the absence of survey evidence on asset lives for Switzerland, this is a sensible approach, and we do not intend to come up with an alternative scheme. Instead, we examine the sensitivity of the results by extending the asset lives listed in Table 1 by 25%. In the 2-asset case, this reduces the depreciation rate from 4% to 3.2% for structures, and from about 13.4% to 10.7% for equipment. Figure 6 displays the results for aggregate capital services and the aggregate capital stock in levels and growth rates. The benchmark results from Section 4 are given for comparison. We can see that raising asset lives by 25% has a significant effect on the level of the capital stock. The capital stock is shifted up because longer asset lives reduce the share of replacement investments (given a time series for gross investment). The level of aggregate capital services, in contrast, does not shift. Again, the volume series is rotated around its 1990 value because the volume of capital services is set equal to total profits in 1990. The growth rates of our capital measures change little when asset lives are extended by 25%. Growth in capital services is just 0.1 pp higher on average over the 1970–2005 period. The annual differences vary between −0.1 pp (1989) and 0.6 pp (1977). Effects on the growth rates of the capital stock are similar.9 6.3 Rate of Return and User Cost of Capital To calculate the user cost of capital according to Equation (8), we need an estimate of the rate of return. The benchmark results reported in Sections 4 and 5 are based on a rate of return derived endogenously from Equation (9). This approach relies on several assumptions which are not strictly realistic. To begin with, markets are assumed to be competitive and returns of scale to be constant to guarantee that the capital services weighted by their user cost of capital exhaust profits. In addition, the assets considered are supposed to account for all sources Measuring Capital Stocks and Capital Services in Switzerland 83 Figure 6: Effect of 25% Increase in Asset Lives on Capital Services and Capital Stock, 2-Asset Case 40 60 80 100 120 140 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02 04 × 1,000 40 60 80 100 120 140 707274767880828486889092949698000204 × 10,000 0 1 2 3 4 5 6 7 Capital services, growth Capital services, growth (benchmark) 707274767880828486889092949698000204 0 1 2 3 4 5 6 7 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02 04 Capital stock, growth Capital stock, growth (benchmark) Capital stock Capital stock (benchmark) Capital services Capital services ( benchmark) 84 Rudolf / Zurlinden of the National Accounts’ gross operating surplus. Finally, agents are assumed to have perfect foresight regarding future prices and interest rates. In the literature, two alternatives have been proposed. First, the rate of return is approximated by some market interest rate for which data are available. This is easy to implement but fraught with the problem that the user cost of capital may turn out to be negative. Additionally, there are many market interest rates and it is not clear which one should be picked. Second, nominal user costs of capital are replaced by real user costs of capital. As argued by Diewert (2003), this simplifies matters since expectations on the real rate of return are likely to be less volatile than expectations on the nominal rate of return. In addition, the risk of obtaining negative user cost of capital is reduced. Both routes are taken up in this section. In the first group of alternative measures of the user cost of capital, we replace the endogenous rate of return from Equation (9) by the government bond yield adjusted by some constant risk premium. Calculations were carried out for risk premiums varying from zero to 4%. It turned out that changes in the constant risk premium appear to have little effect on growth in capital services. Consequently, we will limit ourselves to presenting the results for a 2% risk premium. Two variants are considered. First, asset inflation is assumed to be perfectly anticipated, i.e. the expected one-period asset inflation rate is set equal to the asset inflation observed over that period ex post. This assumption on asset inflation corresponds to the one adopted in Section 2. Second, the expected one-period asset inflation rate is set equal to the 3-year moving average of the asset inflation observed ex post. The second group of alternative measures refers to user cost of capital in real terms. The starting point for the derivation of the formula is Equation (8). Adding and subtracting 1 on the right hand side of the equation gives, after some rearranging, 1 [1 (1 )(1 )] . it t i it it U r qP , , ,− = + − −δ + (19) Let πt denote the rate of change in consumer prices. Dividing both sides of Equation (19) by 1 + πt yields 1 (1 )(1 ) 1. 11 1 it i it t it tt t Uq rP ,, ,− ⎡⎤ −δ + + =− ⎢⎥ +π +π +π ⎣⎦ (20) Measuring Capital Stocks and Capital Services in Switzerland 91 Figure 10 (continued) USP1: capital stock 0 1 2 3 4 5 6 7 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 USP2: capital stock 0 1 2 3 4 5 6 7 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 USP3: capital stock 0 1 2 3 4 5 6 7 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 Capital stock, 12-asset case. US ICT deflators Capital stock, 12-asset case (benchmark) Capital stock, 12-asset case. US ICT deflators adjusted for nominal USD-CHF exchange rate Capital stock, 12-asset case (benchmark) Capital stock, 12-asset case. US ICT deflators adjusted for US-CH price level ratio Capital stock, 12-asset case (benchmark) 92 Rudolf / Zurlinden 12 The latter is computed as the geometric (rather than the arithmetic) mean of the end-of-period asset stocks because the capital stock is assumed to grow at a constant rate within the year. Figure 10 shows the growth rates of aggregate capital services and the aggregate capital stock over the period 1990–2005, based on the three variants of the US price deflators of ICT goods. The results reported in Section 5 are given for comparison. Overall, the results suggest that replacing the national ICT price deflators by the US indices raises growth in aggregate capital services significantly. By contrast, the results for growth in the aggregate capital stock show much smaller differences between the various series. The reason is that, for the three ICT categories, the shares in wealth are much smaller than the shares in profits (see Appendix B for average shares in profits and wealth). 6.5 Mid-year Asset Stocks with Investment Spread Evenly Over the Year We have assumed so far that investment in period t is not depreciated and does not provide capital services in t. According to Equations (1) and (4), both the depreciation and the provision of capital services begin in t + 1 only. If period t is relatively long, this setting gives reasonable results for investments made at the end of the period. But for investments made at the beginning of the period, it implies that they neither depreciate nor provide capital services for a full period. For this reason, the underlying assumptions have been criticised as inadequate in the context of annual data (see e.g. Oulton and Srinivasan, 2003). Alternatively, we can make the explicit assumption that investment is spread evenly across the year. In this case, i-type capital stocks and capital services are determined by 1 (1 ) , it it i it AI A , , ,− = + −δ (23) (1 2) , it i it BA ,, = −δ / (24) 12 1 () it it it it K BB B / , , ,− , == , (25) where Bi,t is the stock of i-type asset at the end of period t when investment are assumed to be done evenly across the the period (see Oulton and Srinivasan, 2003, and Bureau of Economic Analysis, 2003), and it B , is the corresponding stock of i-type asset in the middle of period t.12 Measuring Capital Stocks and Capital Services in Switzerland 93 Figure 11: Capital Services and Capital Stock, Growth Rates, 2-Asset Case and 12-Asset Case: Midyear vs. End of Year (Benchmark Case) 7 6 5 4 3 2 1 0 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02 04 7 6 5 4 3 2 1 0 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 7 6 5 4 3 2 1 0 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02 04 7 6 5 4 3 2 1 0 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 Capital services, 12-asset case, midyear Capital services, 12-asset case (baseline) Capital services, 2-asset case, midyear Capital services, 2-asset case (benchmark) Capital stock, 12-asset case, midyear Capital stock, 12-asset case (benchmark) Capital stock, 2-asset case, midyear Capital xtock, 2-asset case (benchmark) 94 Rudolf / Zurlinden 13 The objection raised in Section 6.5 has less weight when data are quarterly. Thus, we follow Oulton and Srinivasan (2003) and apply the methodology described in Section 2. 14 In the meantime quarterly data on gross operating surplus are published by Seco (see http:// www.seco.admin.ch/themen/00374/00456/00458/index.html?lang=de). Figure 11 shows growth rates of aggregate capital services and the aggregate capital stock calculated based on Equations (23) to (25) replacing Equations (1) and (4), it B , replacing Ai,t in Equation (12), and Bi,t replacing Ai,t in Equation (13). The results from Sections 4 and 5 are given for comparison. The volatility of the series based on mid-year stocks is smaller than that of the benchmark series. And the turning points are in the same period for capital services and the capital stock in the mid-year series (due to ), it it KB , , = whereas capital services lag the capital stock by one period in the measures based on end-of-period asset stocks (due to Ki,t = Ai,t−1). 6.6 Quarterly Estimates In principle, quarterly estimates of capital stocks and capital services can be derived along the same lines as the corresponding annual measures presented in Sections 4 and 5.13 The main difficulty are the data requirements. Whereas quarterly data on investment in total equipment and total structures (2-asset case) are readily available (Seco), data on gross operating surplus and on the 12-asset breakdown of investment are available only annually.14 There are various ways to construct quarterly data from annual data. The results presented below are based on quarterly data for investment volumes derived from the corresponding annual series with the Chow-Lin method. The indicator series are total structures investment for the three structures investment series and total equipment investment for the nine equipment investment series. The twelve asset stocks are then calculated based on the quarterly investment volumes for 1965q1 to 2005q4 and starting values derived from annual data for 1964. The quarterly investment prices are obtained likewise by applying the Chow-Lin method to the annual nominal investment data and dividing the resulting quarterly series by the volume series. Combined with quarterly data for gross operating surplus (obtained by dividing the annual data equally among the four quarters of the year), this allows us to calculate quarterly user costs of capital for the twelve asset stocks. Figure 12 displays the results in terms of annualised quarterly growth rates. The four charts provide a side-by-side comparison of the 2-asset case versus the 12-asset case, and of capital services versus capital stock. Measuring Capital Stocks and Capital Services in Switzerland 95 Figure 12: Capital Services and Capital Stock, Growth Rates, 2-Asset Case and 12-Asset Case: Quarterly Data 4/90 4/92 4/94 4/96 4/98 4/00 4/02 4/04 7 6 5 4 3 2 1 0 Capital services, 2-asset case Capital services, 12-asset case 4/90 4/92 4/94 4/96 4/98 4/00 4/02 4/04 7 6 5 4 3 2 1 0 Capital services, 12-asset case Capital stock, 12-asset case 4/90 4/92 4/94 4/96 4/98 4/00 4/02 4/04 7 6 5 4 3 2 1 0 Capital stock, 2-asset case Capital stock, 12-asset case 1/70 1/75 1/80 1/85 1/90 1/95 1/00 1/05 8 7 6 5 4 3 2 1 0 –1 Capital services, 2-asset case Capital stock, 2-asset case 96 Rudolf / Zurlinden 7. Concluding Remarks In this paper, we have calculated measures of aggregate capital services for the 2-asset case over the period 1970–2005, and for a more detailed breakdown of investment data by 12 categories over the period 1990–2005. These measures have been compared to the corresponding results for the aggregate capital stock, which stands for the wealth concept of capital. The results suggest that the dynamics of capital services calculated from the 12-asset data breakdown are picked up reasonably well by the capital services from the 2-asset breakdown, and even the capital stock from either the 12-asset or 2-asset breakdowns. The differences are not negligible, however, suggesting that a series of capital services calculated from the 12-asset breakdown should be used as a measure of capital input as long as the issue at hand does not require capital data starting earlier than 1990. The calculations for various sets of alternative assumptions suggest that the growth rates of capital services are rather insensitive to changes in the assumptions on starting values and asset lives. The method of calculating the user cost of capital has somewhat larger (but still modest) effects on the results. On the whole, the potential mismeasurement of ICT price deflators might well have been the largest source of uncertainty in recent years. There are various aspects of capital measurement that we have not explored in this paper: – Geometric depreciation has been assumed throughout the work presented here. While there are good arguments for this choice, other forms of depreciation patterns exist and are discussed in the literature (one-hoss-shay, linear, etc.). Diewert (2003) has examined the effect of these assumptions in data for Canada. His findings suggest that the results do not depend critically on the assumption concerning the form of depreciation. – The capital goods considered in this paper are fixed produced assets. Inventories and intangible assets are not considered due to lack of data. Land is not considered either. In a study on Japan, Diewert, Mizobuchi and Nomura (2005) have pointed out that the neglect of land may have a sizable effect on the average growth rate of capital services. Since the volume of land does not usually change much over time, its inclusion reduces growth in the aggregate capital measures. Also, the inclusion of land (and of inventories) may lead to more accurate results for the implied rate of return calculated from gross operating surplus. – The effect of the tax system on the user cost of capital has not been considered in this paper (see Hall and Jorgenson 1967 for an analysis of user cost Measuring Capital Stocks and Capital Services in Switzerland 97 of capital, taking into account the role of taxes). Again, the reason is lack of data. Our results refer to the full economy (with the qualifications described above). Measures of capital for the sectors of the economy cannot be derived for Switzerland, as investment data broken down by industries are not available. What can be calculated, however, are measures of capital that exclude specific forms of fixed assets. For example, residential investment is sometimes excluded from measures of capital input used to calculate potential output growth. Or aggregate capital services are computed for the equipment assets alone and for the structures alone. These aggregates can be calculated easily within the framework described in this paper, which assumes an economy-wide rate of return. Finally, we can compare our results to those published recently by the SFSO. The SFSO begun publishing estimates of growth in capital services in 2006 and of the net capital stock in 2007. Since these series are based on ESVG95 investment data, the corresponding estimates in this paper are the benchmark results for the 12-asset case in Section 5. The most noticeable difference is that the growth rates in capital services tend to differ by one period. This reflects the fact that we assume the flow of capital services services in a given period to be proportional to the stock of capital at the end of the previous period, whereas the SFSO (2006a, p. 7) implicitly assumes proportionality of capital services to the capital stock at the end of the current period. In most other respects the estimates are very similar, which is not surprising given that the methodology does not differ greatly (see Appendix C for a detailed comparison). This said, we have presented various measures of capital for which there is no counterpart in the SFSO publications. Among the data that may prove useful in many areas, we count the longer time series based on two assets (Section 4), the capital services based on mid-year asset stocks and the assumption that investment is spread evenly over the year (Section 6.5), and the quarterly measures of capital (Section 6.6). Looking ahead, we suspect that further progress in measuring capital will depend on better knowledge of asset lives and retirement patterns, the availability of constant-quality price deflators for technology goods, and more complete asset data (land, intangible assets). 98 Rudolf / Zurlinden Appendix A. Data: Definitions and Sources Asset lives. The main source for the assumptions on asset lives is Swiss Federal Statistical Office (2006b). For “growing of crops, market gardening, horticulture, farming of animals”, the authors’ own estimate is used. The SFSO estimate for construction is used for all three components of construction (see Table 1). Consumer price index. Average of monthly observations. Source: SFSO for 1913– 2005; Ritzmann-Blickenstorfer (1996) for 1851–1913. Exchange rate. USD-CHF exchange rate, average of daily observations. Source: SNB. Government bond yield. Average of daily observations. Source: SNB. The exogenous nominal ex-ante rate of return is approximated by the average government bond yield for the previous period. Gross capital formation (investment), volumes and prices. 1948–1990 National Accounts (SFSO) for structures and equipment. 1990–2005 National Accounts ESVG95 (SFSO) for three components of structures (“residential buildings”, “non-residential buildings”, “civil engineering”) and nine components of equipment (“fabricated metal products, machinery and equipment”, “office machinery and computers”, “electrical machinery and apparatus”, “radio, television and communication equipment and apparatus”, “medical, precision and optical instruments, watches and clocks”, “motor vehicles, trailers and semi-trailers”, “other transport equipment”, “computer and related services”, and “growing of crops, market gardening, horticulture, farming of animals”). The data on “nonresidential buildings” is calculated as a residual from data on “buildings” and “residential buildings”. Before 1948: growth rates of investment volumes are approximated by estimates of GDP growth taken from Andrist, Anderson and Williams (2000) for 1913–1948, Ritzmann-Blickenstorfer (1996) for 1851–1913 (gross value added deflated by CPI), and Maddison (2006) for 1820–1851 (based on estimates of the level of real GDP for 1820 and 1851). Growth rates from before 1948 and for 1948–1990 are chain linked to the 1990 data from ESVG95. Investment volumes are at chained 1990 prices. Gross operating surplus. “Gross operating surplus and mixed income” 1990– 2005 from National Accounts (SFSO), for 1970–1990 from OECD National Accounts statistics. Mixed income calculated based on the information on “labour compensation” from the same sources and on the number of self employed and family members from the Labour Force Statistic (SFSO). Measuring Capital Stocks and Capital Services in Switzerland 99 Price deflators for GDP. Source: SFSO for Switzerland, Bureau of Economic Analysis for United States. US price deflators for ICT investment. Price indexes of private fixed investment in equipment and software: “computers”, “software”, “communication equipment”. Source: Bureau of Economic Analysis. B. Asset Stocks, Shares in Profits and in Wealth: 12-Asset Case Table 3 summarises the results for the 12-asset case in terms of average annual growth rates and standard deviations over the period 1990–2005 and two subperiods (1990–2000, 2000–2005). Note that shares in profits are calculated based on Ai,t−1, whereas shares in wealth are calculated based on Ai,t (see Equations (4), (11) and (13)). Table 3: Components of Capital Measures: 12-Asset Case 1990–2005 1990–2000 2000–2005 rate std rate std rate std Residential buildings Capital stock Share in wealth Share in profits 2.09 29.2 20.7 0.68 0.8 2.2 2.28 29.0 20.9 0.65 0.8 2.6 1.70 29.8 20.4 0.64 0.4 1.2 Other buildings Capital stock Share in wealth Share in profits 0.84 27.9 20.0 0.76 1.1 2.4 1.06 28.5 20.7 0.85 0.8 2.5 0.42 26.7 18.6 0.24 0.3 1.1 Civil engineering Capital stock Share in wealth Share in profits 2.49 13.4 9.3 0.94 0.8 2.2 3.02 13.0 9.4 0.63 0.5 2.2 1.44 14.3 9.1 0.35 0.3 2.5 Growing of crops, market gardening, horticulture, farming of animals Capital stock Share in wealth Share in profits 0.47 0.1 0.2 1.91 0.0 0.1 1.00 0.1 0.2 1.42 0.0 0.1 −0.56 0.1 0.2 2.49 0.0 0.1 Fabricated metal products, machinery and equipment Capital stock Share in wealth Share in profits 1.25 15.5 21.8 0.91 0.5 3.1 1.36 15.7 21.9 1.10 0.5 3.7 1.03 15.1 21.7 0.29 0.1 1.7 Office machinery and computers Capital stock Share in wealth Share in profits 5.80 1.0 3.4 3.57 0.1 0.4 6.18 1.0 3.4 4.12 0.0 0.4 5.04 0.9 3.5 2.29 0.1 0.2 100 Rudolf / Zurlinden Table 3 (continued) 1990-2005 1990-2000 2000-2005 rate std rate std rate Std Electrical machinery and apparatus Capital stock Share in wealth Share in profits 0.75 3.0 5.3 1.89 0.3 0.9 1.57 3.2 5.6 0.94 0.2 0.9 −0.88 2.7 4.5 2.37 0.1 0.5 Radio, TV and communication equipment and apparatus Capital stock Share in wealth Share in profits 2.78 2.0 3.8 2.18 0.3 0.6 2.44 2.1 3.9 2.01 0.2 0.6 3.46 1.7 3.6 2.58 0.1 0.3 Medical, precision and optical instruments, watches and clocks Capital stock Share in wealth Share in profits 3.90 3.4 6.0 2.42 0.2 0.8 3.65 3.3 6.0 2.28 0.2 1.0 4.40 3.5 5.9 2.90 0.1 0.5 Motor vehicles, trailers and semi-trailers Capital stock Share in wealth Share in profits 1.61 0.9 1.9 2.38 0.0 0.2 1.55 0.8 1.9 2.73 0.0 0.2 1.72 0.9 2.0 1.76 0.0 0.1 Other transport equipment Capital stock Share in wealth Share in profits 2.53 2.8 3.2 5.27 0.4 1.1 4.64 2.6 2.6 5.22 0.4 0.8 −1.57 3.2 4.3 1.63 0.2 0.5 Computer and related services Capital stock Share in wealth Share in profits 9.25 0.9 4.4 8.66 0.2 1.4 10.11 0.7 3.5 10.16 0.2 0.7 7.54 1.1 6.0 4.81 0.0 0.5 Note: Rate = average rate (growth) or average ratio (share), in percent. Std. = standard deviation. Capital stocks refer to the end of period. C. Comparison with SFSO Series of Aggregate Capital Services and the Aggregate Capital Stock In October 2006, the SFSO published estimates of growth in multi-factor productivity for the years 1991 to 2004; see Swiss Federal Statistical Office (2006b) and Rais and Sollberger (2006). One year later, the data were revised and updated to 2005. These productivity estimates are based on estimates of growth in capital services as measures of capital input. Also, in October 2006, the SFSO published estimates of the gross capital stock; see Swiss Federal